2000 character limit reached
Decay-protected superconducting qubit with fast control enabled by integrated on-chip filters
Published 14 Feb 2024 in quant-ph | (2402.08906v2)
Abstract: Achieving fast gates and long coherence times for superconducting qubits presents challenges, typically requiring either a stronger coupling of the drive line or an excessively strong microwave signal to the qubit. To address this, we introduce on-chip filters of the qubit drive exhibiting a stopband at the qubit frequency, thus enabling long coherence times and strong coupling at the subharmonic frequency, facilitating fast single-qubit gates, and reduced thermal load. The filters exhibit an extrinsic relaxation time of a few seconds while enabling sub-10-ns gates with subharmonic control. Here we show up to 200-fold improvement in the measured relaxation time at the stopband. Furthermore, we implement subharmonic driving of Rabi oscillations with a $\pi$ pulse duration of 12 ns. Our demonstration of on-chip filters and efficient subharmonic driving in a two-dimensional quantum processor paves the way for a scalable qubit architecture with reduced thermal load and noise from the control line.
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URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. 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Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. 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[9] Burkard, G., Ladd, T. D., Pan, A., Nichol, J. M. & Petta, J. R. Semiconductor spin qubits. Reviews of Modern Physics 95, 025003 (2023). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.95.025003. [10] Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001). URL https://www.nature.com/articles/35051009. [11] Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). 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URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Weinstein, A. J. et al. Universal logic with encoded spin qubits in silicon. Nature 615, 817–822 (2023). URL https://www.nature.com/articles/s41586-023-05777-3. [9] Burkard, G., Ladd, T. D., Pan, A., Nichol, J. M. & Petta, J. R. Semiconductor spin qubits. Reviews of Modern Physics 95, 025003 (2023). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.95.025003. [10] Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001). URL https://www.nature.com/articles/35051009. [11] Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. 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[14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). 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[23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. 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Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001). URL https://www.nature.com/articles/35051009. [11] Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. 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URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. 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URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. 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URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. 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URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. 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Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. 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URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. 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Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. 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[9] Burkard, G., Ladd, T. D., Pan, A., Nichol, J. M. & Petta, J. R. Semiconductor spin qubits. Reviews of Modern Physics 95, 025003 (2023). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.95.025003. [10] Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001). URL https://www.nature.com/articles/35051009. [11] Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. 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URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Weinstein, A. J. et al. Universal logic with encoded spin qubits in silicon. Nature 615, 817–822 (2023). URL https://www.nature.com/articles/s41586-023-05777-3. [9] Burkard, G., Ladd, T. D., Pan, A., Nichol, J. M. & Petta, J. R. Semiconductor spin qubits. Reviews of Modern Physics 95, 025003 (2023). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.95.025003. [10] Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001). URL https://www.nature.com/articles/35051009. [11] Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. 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[14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. 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Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001). URL https://www.nature.com/articles/35051009. [11] Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. 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Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. 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URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. 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URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). 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URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. 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URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. 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Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. 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URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bluvstein, D. et al. A quantum processor based on coherent transport of entangled atom arrays. Nature 604, 451–456 (2022). URL https://www.nature.com/articles/s41586-022-04592-6. [5] Bluvstein, D. et al. Logical quantum processor based on reconfigurable atom arrays. Nature 1–8 (2023). URL https://www.nature.com/articles/s41586-023-06927-3. [6] Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Physical Review A - Atomic, Molecular, and Optical Physics 57, 120–126 (1998). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.57.120. [7] Xue, X. et al. Quantum logic with spin qubits crossing the surface code threshold. Nature 601, 343–347 (2022). URL https://www.nature.com/articles/s41586-021-04273-w. [8] Weinstein, A. J. et al. Universal logic with encoded spin qubits in silicon. Nature 615, 817–822 (2023). URL https://www.nature.com/articles/s41586-023-05777-3. [9] Burkard, G., Ladd, T. D., Pan, A., Nichol, J. M. & Petta, J. R. Semiconductor spin qubits. Reviews of Modern Physics 95, 025003 (2023). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.95.025003. [10] Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001). URL https://www.nature.com/articles/35051009. [11] Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. 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Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bluvstein, D. et al. Logical quantum processor based on reconfigurable atom arrays. Nature 1–8 (2023). URL https://www.nature.com/articles/s41586-023-06927-3. [6] Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Physical Review A - Atomic, Molecular, and Optical Physics 57, 120–126 (1998). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.57.120. [7] Xue, X. et al. Quantum logic with spin qubits crossing the surface code threshold. Nature 601, 343–347 (2022). URL https://www.nature.com/articles/s41586-021-04273-w. [8] Weinstein, A. J. et al. Universal logic with encoded spin qubits in silicon. Nature 615, 817–822 (2023). URL https://www.nature.com/articles/s41586-023-05777-3. [9] Burkard, G., Ladd, T. D., Pan, A., Nichol, J. M. & Petta, J. R. Semiconductor spin qubits. Reviews of Modern Physics 95, 025003 (2023). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.95.025003. [10] Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001). URL https://www.nature.com/articles/35051009. [11] Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). 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URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. 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Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. 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Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. 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URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. 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URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. 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URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. 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URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). 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URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. 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Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. 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URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. 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URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Xue, X. et al. Quantum logic with spin qubits crossing the surface code threshold. Nature 601, 343–347 (2022). URL https://www.nature.com/articles/s41586-021-04273-w. [8] Weinstein, A. J. et al. Universal logic with encoded spin qubits in silicon. Nature 615, 817–822 (2023). URL https://www.nature.com/articles/s41586-023-05777-3. [9] Burkard, G., Ladd, T. D., Pan, A., Nichol, J. M. & Petta, J. R. 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URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.95.025003. [10] Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001). URL https://www.nature.com/articles/35051009. [11] Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001). URL https://www.nature.com/articles/35051009. [11] Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. 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Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. 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URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. 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[23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. 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Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. 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URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). 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Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). 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[9] Burkard, G., Ladd, T. D., Pan, A., Nichol, J. M. & Petta, J. R. Semiconductor spin qubits. Reviews of Modern Physics 95, 025003 (2023). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.95.025003. [10] Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001). URL https://www.nature.com/articles/35051009. [11] Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). 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URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). 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Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burkard, G., Ladd, T. D., Pan, A., Nichol, J. M. & Petta, J. R. Semiconductor spin qubits. Reviews of Modern Physics 95, 025003 (2023). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.95.025003. [10] Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001). URL https://www.nature.com/articles/35051009. [11] Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001). URL https://www.nature.com/articles/35051009. [11] Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). 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URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). 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Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. 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Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. 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URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. 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URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. 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URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. 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Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. 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URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. 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Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. 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[9] Burkard, G., Ladd, T. D., Pan, A., Nichol, J. M. & Petta, J. R. Semiconductor spin qubits. Reviews of Modern Physics 95, 025003 (2023). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.95.025003. [10] Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001). URL https://www.nature.com/articles/35051009. [11] Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. 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URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. 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The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001). URL https://www.nature.com/articles/35051009. [11] Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. 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URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). 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URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. 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URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. 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[38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. 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URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. 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Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. 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URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). 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URL https://www.nature.com/articles/s41467-022-34614-w. Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. 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Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. 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Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. 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URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). 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URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. 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The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. 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J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). 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Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. 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URL https://www.nature.com/articles/35051009. [11] Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001). URL https://www.nature.com/articles/35051009. [11] Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. 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URL https://www.nature.com/articles/s41467-022-34614-w. Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. 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[38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. 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Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. 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Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). 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URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. 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The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. 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URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. 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URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. 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URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). 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Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. 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URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. 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[14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). 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[23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. 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URL https://www.nature.com/articles/s41467-022-34614-w. Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). 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URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. 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The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. 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Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. 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J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. 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URL https://www.nature.com/articles/s41467-022-34614-w. Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Physical Review Letters 95, 010501 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.010501. [12] O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007). URL https://www.science.org/doi/10.1126/science.1142892. [13] Shi, S. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source. Nature Communications 13, 1–6 (2022). URL https://www.nature.com/articles/s41467-022-32083-9. [14] Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. [16] Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. 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URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. 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The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). 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URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999). URL https://www.nature.com/articles/19718. [15] Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A - Atomic, Molecular, and Optical Physics 76, 042319 (2007). URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.042319. 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Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). 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URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). 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URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. 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URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. 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[59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. 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URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). 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[38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. 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Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). 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URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. 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The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. 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URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. 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URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. 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URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. 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Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). 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URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). 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URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. 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URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. 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URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. 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Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. 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URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). 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[38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). 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URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. 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The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. 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URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. 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URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. 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[22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. 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The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). 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Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Devoret, M. H. & Martinis, J. M. Implementing qubits with superconducting integrated circuits. Experimental Aspects of Quantum Computing 3, 163–203 (2005). URL https://link.springer.com/article/10.1007/s11128-004-3101-5. [17] Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kockum, A. F. & Nori, F. Quantum Bits with Josephson Junctions. Springer Series in Materials Science 286, 703–741 (2019). URL https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17. [18] Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). 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[38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. 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URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). 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Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. 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Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. 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URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. 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URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. 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Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. 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URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. 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URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). 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URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. 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The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. 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Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. 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J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. 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A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). 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URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bladh, K., Duty, T., Gunnarsson, D. & Delsing, P. The single Cooper-pair box as a charge qubit. New Journal of Physics 7, 180 (2005). URL https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180/meta. [19] Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds. npj Quantum Information 8, 1–6 (2022). URL https://www.nature.com/articles/s41534-021-00510-2. [20] Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. 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Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Verjauw, J. et al. Path toward manufacturable superconducting qubits with relaxation times exceeding 0.1 ms. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00600-9. [21] Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. 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Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. 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URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nature Communications 12, 1–6 (2021). URL https://www.nature.com/articles/s41467-021-22030-5. [22] Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. 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URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). 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Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. 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Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. 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URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. 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URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Somoroff, A. et al. Millisecond Coherence in a Superconducting Qubit. Physical Review Letters 130, 267001 (2023). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.267001. [23] Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. 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The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). 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Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. 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Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information 7, 1–6 (2021). URL https://www.nature.com/articles/s41534-020-00346-2. [24] Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Ding, L. et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler. Physical Review X 13, 031035 (2023). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031035. [25] Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. 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URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). 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Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. 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A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. 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Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. 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Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. 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Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. 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URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). 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[59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. 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Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. 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Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric Loss. Physical Review Letters 95, 210503 (2005). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.210503. [26] Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. 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Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. 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URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Gao, J. et al. A semiempirical model for two-level system noise in superconducting microresonators. Applied Physics Letters 92, 212504 (2008). URL /aip/apl/article/92/21/212504/851718/A-semiempirical-model-for-two-level-system-noise. [27] Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. 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URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. 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Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. 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URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lindström, T., Healey, J. E., Colclough, M. S., Muirhead, C. M. & Tzalenchuk, A. Y. Properties of superconducting planar resonators at millikelvin temperatures. Physical Review B - Condensed Matter and Materials Physics 80, 132501 (2009). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.132501. [28] Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. 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[38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. 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[37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. 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URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Macha, P. et al. Losses in coplanar waveguide resonators at millikelvin temperatures. Applied Physics Letters 96, 62503 (2010). URL /aip/apl/article/96/6/062503/167025/Losses-in-coplanar-waveguide-resonators-at. [29] Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Transactions on Applied Superconductivity 21, 871–874 (2011). [30] Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Neill, C. et al. Fluctuations from edge defects in superconducting resonators. Applied Physics Letters 103, 72601 (2013). URL /aip/apl/article/103/7/072601/150361/Fluctuations-from-edge-defects-in-superconducting. [31] Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. 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Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. 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URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. 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[57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. 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Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w.
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URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Physical Review B - Condensed Matter and Materials Physics 92, 035442 (2015). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.035442. [32] Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Applied Physics Letters 107, 162601 (2015). URL /aip/apl/article/107/16/162601/593971/Surface-participation-and-dielectric-loss-in. [33] Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). 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Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. 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Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. 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Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lutchyn, R. M., Glazman, L. I. & Larkin, A. I. Kinetics of the superconducting charge qubit in the presence of a quasiparticle. Physical Review B - Condensed Matter and Materials Physics 74, 064515 (2006). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.064515. [34] Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. 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The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). 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URL https://www.nature.com/articles/s41467-022-34614-w. Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. 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Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. 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Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w.
- Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Physical Review Letters 107, 240501 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.240501. [35] Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Physical Review Letters 106, 077002 (2011). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.077002. [36] Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Physical Review B - Condensed Matter and Materials Physics 86, 184514 (2012). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.184514. [37] Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. L. 1/ f noise: Implications for solid-state quantum information. Reviews of Modern Physics 86, 361–418 (2014). URL https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.361. [38] Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. 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URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. 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URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. 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Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. 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URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). 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URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. 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URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. 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Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Burnett, J. et al. Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator. Nature Communications 5, 1–6 (2014). URL https://www.nature.com/articles/ncomms5119. [39] Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). URL https://www.nature.com/articles/nature13017. [40] Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. 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URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). 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[59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. 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Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. 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Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. 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Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). 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[52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. 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Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. 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URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. 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Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). 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URL https://www.nature.com/articles/s41467-022-34614-w. Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w.
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Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. 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URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Information 5, 1–6 (2019). URL https://www.nature.com/articles/s41534-019-0224-1. [41] Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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[43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). 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[63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w.
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Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications 7, 1–9 (2016). URL https://www.nature.com/articles/ncomms12964. [42] Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). 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[64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w.
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URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020). URL https://www.nature.com/articles/s41586-020-2619-8. [43] Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Murray, C. E. Material matters in superconducting qubits. Materials Science and Engineering R: Reports 146, 100646 (2021). [44] Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. 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Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. 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URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. 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B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Siddiqi, I. Engineering high-coherence superconducting qubits. Nature Reviews Materials 6, 875–891 (2021). URL https://www.nature.com/articles/s41578-021-00370-4. [45] Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Carroll, M., Rosenblatt, S., Jurcevic, P., Lauer, I. & Kandala, A. Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). 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URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. 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URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. 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Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. 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URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w.
- Dynamics of superconducting qubit relaxation times. npj Quantum Information 8, 1–7 (2022). URL https://www.nature.com/articles/s41534-022-00643-y. [46] Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Applied Physics Letters 95, 233508 (2009). URL /aip/apl/article/95/23/233508/120944/Improving-the-coherence-time-of-superconducting. [47] Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w.
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Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. 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Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Megrant, A. et al. Planar superconducting resonators with internal quality factors above one million. Applied Physics Letters 100, 113510 (2012). URL /aip/apl/article/100/11/113510/126200/Planar-superconducting-resonators-with-internal. [48] Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Applied Physics Letters 103, 12602 (2013). URL /aip/apl/article/103/1/012602/235870/Improved-superconducting-qubit-coherence-using. [49] Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Stern, M. et al. Flux qubits with long coherence times for hybrid quantum circuits. Physical Review Letters 113, 123601 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.123601. [50] Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. 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[57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. 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Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. 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Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). 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Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. 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URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. 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Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. 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Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). 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Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Xia, M. et al. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. 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URL https://www.nature.com/articles/s41467-022-34614-w. Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. 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URL https://www.nature.com/articles/s41467-022-34614-w. Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Hyyppä, E. et al. 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URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Bruno, A. et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates. Applied Physics Letters 106, 182601 (2015). URL /aip/apl/article/106/18/182601/27784/Reducing-intrinsic-loss-in-superconducting. [51] Deng, H. et al. Titanium Nitride Film on Sapphire Substrate with Low Dielectric Loss for Superconducting Qubits. Physical Review Applied 19, 024013 (2023). URL https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.024013. [52] He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). 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Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. 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Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. 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URL https://www.nature.com/articles/s41467-022-34614-w. Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Hyyppä, E. et al. 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[57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. 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Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. He, H., Wang, W., Liu, F., Yuan, B. & Shan, Z. Suppressing the Dielectric Loss in Superconducting Qubits through Useful Geometry Design. Entropy 24, 952 (2022). URL https://www.mdpi.com/1099-4300/24/7/952/htmhttps://www.mdpi.com/1099-4300/24/7/952. [53] Martinis, J. M. 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Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Martinis, J. M. Surface loss calculations and design of a superconducting transmon qubit with tapered wiring. npj Quantum Information 8, 1–12 (2022). URL https://www.nature.com/articles/s41534-022-00530-6. [54] Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. 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URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. 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Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w.
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Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Krinner, S. et al. Engineering cryogenic setups for 100-qubit scale superconducting circuit systems. EPJ Quantum Technology 6 (2019). URL https://doi.org/10.1140/epjqt/s40507-019-0072-0. [55] Kono, S. et al. Breaking the trade-off between fast control and long lifetime of a superconducting qubit. Nature Communications 11, 1–6 (2020). URL https://www.nature.com/articles/s41467-020-17511-y. [56] Xia, M. et al. Fast superconducting qubit control with sub-harmonic drives (2023). URL http://arxiv.org/abs/2306.10162. [57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. 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[57] Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. 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URL https://www.nature.com/articles/s41467-022-34614-w. Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Physical Review Letters 111, 080502 (2013). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.080502. [58] Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. 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URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). 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URL https://www.nature.com/articles/s41467-022-34614-w. Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. 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URL https://www.nature.com/articles/s41467-022-34614-w. Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Hyyppä, E. et al. 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Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w.
- Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Physical Review Letters 112, 190504 (2014). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.190504. [59] Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w.
- Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Physical Review B 34, 158–163 (1986). URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.34.158. [60] Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w.
- Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Physical Review Letters 101, 080502 (2008). URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.080502. [61] Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w.
- Circuit quantum electrodynamics. Reviews of Modern Physics 93, 025005 (2021). [62] Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Fedorov, G. P. & Ustinov, A. V. Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w.
- Automated analysis of single-tone spectroscopic data for cQED systems. Quantum Science and Technology 4, 045009 (2019). URL https://iopscience.iop.org/article/10.1088/2058-9565/ab478bhttps://iopscience.iop.org/article/10.1088/2058-9565/ab478b/meta. [63] Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w.
- Zhang, H. et al. Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit. Physical Review X 11, 011010 (2021). URL https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011010. [64] Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w. Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w.
- Hyyppä, E. et al. Unimon qubit. Nature Communications 13, 1–14 (2022). URL https://www.nature.com/articles/s41467-022-34614-w.
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